Journal ArticleDOI
A Bandwidth Selector for Bivariate Kernel Regression
TLDR
This paper proposes a selector based on an iterative plug-in approach for bivariate kernel regression that is shown to give satisfactory results and can be quickly computed.Abstract:
SUMMARY For two and higher dimensional kernel regression, currently available bandwidth selection procedures are based on cross-validation or related penalizing ideas. However, these techniques have been shown to suffer from high sample variability and, in addition, can sometimes be difficult to implement when a vector of bandwidths needs to be selected. In this paper we propose a selector based on an iterative plug-in approach for bivariate kernel regression. It is shown to give satisfactory results and can be quickly computed. Our ideas can be extended to higher dimensions.read more
Citations
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Journal ArticleDOI
On difference‐based variance estimation in nonparametric regression when the covariate is high dimensional
TL;DR: In this paper, the authors consider the problem of estimating the noise variance in homoscedastic nonparametric regression models and show that for finite sample sizes, the performance of these estimators may be deficient owing to a large finite sample bias.
Journal ArticleDOI
Multiscale methods for data on graphs and irregular multidimensional situations
TL;DR: In this paper, the concept of scale was introduced as a continuous quantity rather than dyadic levels, and the wavelet transform was adapted for function estimation both on graphs and for irregular spatial data in more than one dimension.
Journal ArticleDOI
Multivariate bandwidth selection for local linear regression
Lijian Yang,Rolf Tschernig +1 more
TL;DR: In this article, the existence and properties of optimal bandwidths for multivariate local linear regression are established, using either a scalar bandwidth for all regressors or a diagonal bandwidth vector that has a different bandwidth for each regressor.
Journal ArticleDOI
Consistency and rates of convergence of nonlinear Tikhonov regularization with random noise
TL;DR: In this paper, the authors consider nonlinear inverse problems described by operator equations F(a) = u and construct an estimator for a by a combination of a local polynomial estimator and a nonlinear Tikhonov regularization.
Journal ArticleDOI
Estimation of the sea state bias in radar altimeter measurements of sea level: Results from a new nonparametric method
TL;DR: In this article, a nonparametric version of the sea state bias (SSB) estimation problem was proposed based on the statistical technique of kernel smoothing, which was then used to obtain the first fully non-parametric estimate of the TOPEX altimeter SSB as a function of both the wind speed and the wave height.
References
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Book
Applied Nonparametric Regression
TL;DR: This chapter discusses smoothing in high Dimensions, Investigating multiple regression by additive models, and incorporating parametric components and alternatives.
Journal ArticleDOI
A reliable data-based bandwidth selection method for kernel density estimation
Simon J. Sheather,M. C. Jones +1 more
TL;DR: The key to the success of the current procedure is the reintroduction of a non- stochastic term which was previously omitted together with use of the bandwidth to reduce bias in estimation without inflating variance.
Posted Content
Applied Nonparametric Regression
TL;DR: Applied Nonparametric Regression is the first book to bring together in one place the techniques for regression curve smoothing involving more than one variable and argues that all smoothing methods are based on a local averaging mechanism and can be seen as essentially equivalent to kernel smoothing.